text:
Community structure is ubiquitous in biological networks. There has been an increased interest in unraveling the community structure of biological systems as it may provide important insights into a system's functional components and the impact of local structures on dynamics at a global scale. Choosing an appropriate community detection algorithm to identify the community structure in an empirical network can be difficult, however, as the many algorithms available are based on a variety of cost functions and are difficult to validate. Even when community structure is identified in an empirical system, disentangling the effect of community structure from other network properties such as clustering coefficient and assortativity can be a challenge.
Here, we develop a generative model to produce undirected, simple, connected graphs with a specified degrees and pattern of communities, while maintaining a graph structure that is as random as possible. Additionally, we demonstrate two important applications of our model: (a) to generate networks that can be used to benchmark existing and new algorithms for detecting communities in biological networks; and (b) to generate null models to serve as random controls when investigating the impact of complex network features beyond the byproduct of degree and modularity in empirical biological networks.
Our model allows for the systematic study of the presence of community structure and its impact on network function and dynamics. This process is a crucial step in unraveling the functional consequences of the structural properties of biological systems and uncovering the mechanisms that drive these systems.
Keywords:Biological networks; Community structure; Random graphs; Modularity; Benchmark graphs
Network analysis and modeling is a rapidly growing area which is moving forward our understanding of biological processes. Networks are mathematical representations of the interactions among the components of a system. Nodes in a biological network usually represent biological units of interest such as genes, proteins, individuals, or species. Edges indicate interaction between nodes such as regulatory interaction, gene flow, social interactions, or infectious contacts [1]. A basic model for biological networks assumes random mixing between nodes of the network. The network patterns in real biological populations, however, are typically more heterogeneous than assumed by these simple models [2]. For instance, biological networks often exhibit properties such as degree heterogeneity, assortative mixing, non-trivial clustering coefficients, and community structure (see review by Proulx et al. [1]). Of particular interest is community structure, which reflects the presence of large groups of nodes that are typically highly connected internally but only loosely connected to other groups [3,4]. This pattern of large and relatively dense subgraphs is called assortative community structure. In empirical networks, these groups, also called modules or communities, often correspond well with experimentally-known functional clusters within the overall system. Thus, community detection, by examining the patterns of interactions among the parts of a biological system, can help identify functional groups automatically, without prior knowledge of the system's processes.
Although community structure is believed to be a central organizational pattern in biological networks such as metabolic [5], protein [6,7], genetic [8], food-web [9,10] and pollination networks [11], a detailed understanding of its relationship with other network topological properties is still limited. In fact, the task of clearly identifying the true community structure within an empirical network is complicated by a multiplicity of community detection algorithms, multiple and conflicting definitions of communities, inconsistent outcomes from different approaches, and a relatively small number of networks for which ground truth is known. Although node attributes in empirical networks (e.g., habitat type in foodwebs) are sometimes used to evaluate the accuracy of community detection methods [12], these results are generally of ambiguous value as the failure to recover communities that correlates with some node attribute may simply indicate that the true features driving the network's structure are unobserved, not that the identified communities are incorrect.
A more straightforward method of exploring the structural and functional role of a network property is to generate graphs which are random with respect to other properties except the one of interest. For example, network properties such as degree distribution, assortativity and clustering coefficient have been studied using the configuration model [13], and models for generating random graphs with tunable structural features [2,14,15]. These graphs serve to identify the network measures that assume their empirical values in a particular network due to the particular network property of interest. In this work, we propose a model for generating simple, connected random networks that have a specified degree distribution and level of community structure.
Random graphs with tunable strength of community structure can have several purposes such as: (1) serving as benchmarks to test the performance of community detection algorithms; (2) serving as null models for empirical networks to investigate the combined effect of the observed degrees and the latent community structure on the network properties; (3) serving as proxy networks for modeling network dynamics in the absence of empirical network data; and (4) allowing for the systematic study of the impact of community structure on the dynamics that may flow on a network. Among these, the use of random graphs with tunable strength of community structure to serve as benchmarks has received the most attention and several such models have been proposed [16-21]. A few studies have also looked at the role of community structure in the flow of disease through contact networks [22-25]. However, the use of modular random graphs, which can be defined as random graphs that have a higher strength of community structure than what is expected at random, is still relatively unexplored in other applications.
Previous work
In 2002, Girvan and Newman proposed a simple toy model for generating random networks with a specific configuration and strength of community structure [3]. This model assumes a fixed number of modules each of equal size and where each node in each module has the same degree. In this way, each module is an Erdős-Rényi random graph. To produce modular structure, different but fixed probabilities are used to produce edges within or between modules. Although this toy model has been widely used to evaluate the accuracy of community detection algorithms, it has limited relevance to real-world networks, which are generally both larger and much more heterogeneous. Lancichinetti et al. [16] introduced a generalization of the Girvan-Newman model that better incorporates some of these features, e.g., by including heterogeneity in both degree and community size. However, this model assumes that degrees are always distributed in a particular way (like a power law [26]), which is also unrealistic. (A similar model by Bagrow [17] generates modular networks with power law degree distribution and constant community size.)
Yan et al. [23] used a preferential attachment model to grow scale-free networks comprised of communities of nodes whose degrees follow a power-law distribution. And, models for special graph types such as hierarchical networks [18], bipartite networks [21], and networks with overlapping modules [20] have also been proposed. These models also make strong assumptions about the degree or community size distributions, which may not be realistic for comparison with real biological networks. A recently proposed model [19] does generate networks with a broad range of degree distributions, modularity and community sizes, but its parameters have an unclear relationship with desired properties (such as degree distribution and modularity), making it difficult to use in practice. Thus, while these models may be sufficient for comparative evaluation of community detection algorithms, they are of limited value for understanding their performance and output when applied to real-world networks.
An alternative approach comes from probabilistic models, of which there are two popular classes. Exponential random graph models (ERGMs) have a long history of use in social network analysis, and can generate an ensemble of networks that contain certain frequencies of local graph features, including heterogeneous degrees, triangles, and 4-cycles [27]. However, many classes of ERGMs exhibit pathological behavior when parameterized with triangles or higher-order structures [28], which severely limits their utility. Stochastic block models (SBMs) are more promising, but require a large number of parameters to be chosen before a graph can be generated. In this approach, the probability of each link depends only on the community labels of its endpoints. Thus, to generate a network, we must specify the number of communities K, their sizes (in the form of a labeling of the vertices), and the (in the undirected case) group-pair probabilities. The result is a random graph with specified community sizes, where each community is an Erdős-Rényi random graph with a specified internal density, and each pair of communities is a random bipartite graph with specified density. The degree distributions of these networks is a mixture of Poisson distributions, which can be unrealistic. A recent generalization of the SBM due to Karrer and Newman [29] allows the specification of the degree sequence, which circumvents this limitation but introduces another set of parameters to be chosen. Although the stochastic block models can in principle be used to generate synthetic networks, they are more commonly used within an inferrential framework in which community structure is recovered by estimating the various parameters directly from a network. As a result, the practical use of the SBM as a null model, either for general benchmarking of community detection algorithms or for understanding the structure of biological networks, remains largely unexplored, and we lack clear answers as to how best to sample appropriately from its large parameter space in these contexts. The SBM also does not provide a simple measure of the level of modularity in a network's large-scale structure, which makes its structure more difficult to interpret. The SBM is a promising model for many tasks, and adapting it to the questions we study here remains an interesting avenue for future work.
Our approach
Here, we develop and implement a simple simulation model for generating modular random graphs using only a small number of intuitive and interpretable parameters. Our model can generate graphs over a broad range of distributions of network degree and community size. The generated graphs can range from very small (<102) to large (> 105) network sizes and can be composed of a variable number of communities. In Methods below, we introduce our algorithm for generating modular random graphs. In Results and discussion, we consider the performance of our algorithm and structural features of our generated graphs to show that properties such as degree assortativity, clustering, and path length remain unchanged for increasing modularity. We next demonstrate the applicability of the generated modular graphs to test the accuracy of extant community detection algorithms. The accuracy of community detection algorithms depends on several network properties such as the network mean degree and strength of community structure, which is evident in our analysis. Finally, using a few empirical biological networks, we demonstrate that our model can be used to generate corresponding null modular graphs under two different models of randomization. We conclude the paper with some thoughts about other applications and present some future directions.
We present a model that generates undirected, simple, connected graphs with prescribed degree sequences and a specified level of community structure, while maintaining a graph structure that is otherwise as random (uncorrelated) as possible. Below, we introduce some notation and a metric for measuring community structure, followed by a description of our model and the steps of the algorithm used to generate graphs with this specified structure.
Measure of community structure
We begin with a graph G=(V,E) that is comprised of a set of vertices or nodes V(G)={v1,…,vn} and a set of edges E(G)={e1,…,em}. G is undirected and simple (i.e. a maximum of one edge is allowed between a pair of distinct nodes, and no "self" edges are allowed). The number of nodes and edges in G is |V(G)|=n and |E(G)|=m, respectively. The neighborhood of a node vi is the set of nodes vi is connected to, N(vi)={vj | (vi,vj)∈E,vi≠vj,1≤j≤n}. The degree of a node vi, or the size of the neighborhood connected to vi, is denoted as d(vi)=|N(vi)|. A degree sequence, D, specifies the set of all node degrees as tuples, such that D={(vi,d(vi)} and follows a probability distribution called the degree distribution with mean .
Each community or moduleCk is defined as a subset of G that contains both nodes, V(Ck) and edges E(Ck), where both the endpoints of each edge in E(Ck) are contained in V(Ck). K is the number of modules in G and k ∈[ 1,K]. Each node vi of G has a within-degree, dw(vi)=|N(vi)∩V(Ck)|, which is the number of within-edges connecting vi to other nodes of the same module Ck; and a between-degree, db(vi)=|N(vi)−V(Ck)|, i.e. the number of between-edges connecting vi to nodes in different modules (here, the minus operator represents set difference). The strength of the community structure defined by a partition, {Ck}, can be measured as modularity, Q, and is defined as
where denotes the proportion of all edges that are within module Ck, and represents the fraction of all edges that touch nodes in community Ck. When Q=0, the density of within-community edges is equivalent to what is expected when edges are distributed at random, conditioned on the given degree sequence. Values approaching Q=1, which is the maximum possible value of Q, indicate networks with strong community structure. Typically, values for empirical network modularity fall in the range from about 0.3 to 0.7 [30]. However, in theory Good et al. [31] show that maximum Q values depend on the network size and number of modules.
In order to generate a graph with a specified strength of community structure, Q, equation (1) represents our first constraint, which we rewrite below in terms of the expected value of Q, (full derivation in Additional file 1):
Additional file 1. Supplementary analysis. Additional analysis of algorithm with figures.
Format: PDF Size: 1.5MB Download file
This file can be viewed with: Adobe Acrobat Reader
where and are the average within-degree and average degree, respectively, and sk=|V(Ck)| is the module size for module k. Thus, equation (2) allows us to specify in terms of Q, , m and sk, assuming that the module-specific average degree and average within-degree are equal to and , respectively. When for all k, E[Q] reduces to .
We note that as the average within-degree () approaches the average degree (), the graph, G becomes increasingly modular. Hence, the maximum modularity for G with K modules can be estimated as:
We present a model and an algorithm that generates undirected, unweighted, simple and connected modular random graphs. The model is specified by a network size (n), degree distribution (pd), an expected modularity (E[Q]), the number of modules (K), and the module size distribution (P(s)), with mean . (We note a degree sequence, d(vi), may be specified instead of a degree distribution, pd). The algorithm proceeds in four steps:
1. Assign the n network nodes to K modules based on the size distribution P(s).
2. Assign degrees, d(vi), to each node vi based on pd and . We next assign within-degrees, dw(vi), to each node vi by assuming that the within-degrees follow the same distribution as pd with mean , which is estimated based on equation (2) above (Figure 1a).3. Connect between-edges based on a modified Havel-Hakimi model and randomize them (Figure 1b).4. Connect within-edges based on the Havel-Hakimi model and randomize them (Figure 1c and 1d).
Figure 1. Schematic representation of the steps of our algorithm.(a) The algorithm assigns a within-degree and between-degree to each node, which are represented here as half-within-edges and half-between-edges respectively. (b) The half-between-edges are then connected using a modified version of the Havel-Hakimi algorithm, and to remove degree correlations, the between-edges are randomized. (c) Finally, the half-within-edges are connected using the standard Havel-Hakimi algorithm for each module and (d) the within-edges are randomized to remove degree correlations.
The generated graph then has a degree distribution that follows pd with mean , K modules with sizes distributed as P(s), and a modularity Q≈E[ Q]. We set an arbitrary tolerance of ε=0.01, such that the achieved modularity is Q=E[ Q]± ε. The graph is also as random as possible given the constraints of the degree and community structure, contains no self loops (edges connecting a node to itself), multi-edges (multiple edges between a pair of nodes), isolate nodes (nodes with no edges), or disconnected components. Below, we elaborate on each of the steps of this algorithm.
Assigning nodes to modules
We sample module sizes, sk, for each of the K modules from the specified module size distribution, P(s) so that . The n nodes are then arbitrarily (without loss of generality) assigned to each module to satisfy the sampled module size sequence.
Assigning degrees
Based on the degree distribution specified, a degree sequence is sampled from the distribution to generate a degree, d(vi), for each node vi (unless a degree sequence is already specified in the input). To ensure that the degree sequence attains the expected mean of the distribution (within a specified threshold) and is realizable, we verify the Handshake Theorem (the requirement that the sum of the degrees be even) and the Erdős-Gallai criterion (which requires that for each subset of the k highest degree nodes, the degrees of these nodes can be "absorbed" within the subset and the remaining degrees) [32], and that no node is assigned a degree of zero.
Unless a within-degree sequence is specified, we assume that the within-degree distribution follows the class of the degree distribution specified, pd, with mean based on equation (2) (i.e. a generated network with a Poisson degree distribution of mean also has a Poisson within-degree distribution with mean ). This assumption is considered reasonable as it holds true for several of the empirical networks we analyze (shown in Figure S1 in Additional file 1). However, our model can be extended for arbitrary within-degree distributions (or sequences) (see Table S1 in Additional file 1), although the space of feasible within-degree distributions given a degree distribution is restricted. Next, we sample a within-degree sequence, dw(vi), from this within-degree distribution. Using rejection sampling, we ensure that the within-degree sequence attains the expected overall mean, within a tolerance (with details in the Additional file 1), and satisfies the following conditions:
● Condition 1: d(vi)≥dw(vi) for all vi. To ensure this, we sort the degree sequence and within-degree sequence, independently. If d(vi)<dw(vi) for any vi in the ordered lists, the condition is not satisfied. In Figure S2 of Additional file 1, we discuss the rejection rates for the rejection sampling of both the degree and within-degree sequence.
● Condition 2: a realizable within-degree sequence for each module, Ck, as defined by the Handshake Theorem and the Erdos-Gallai criterion.
In addition, to ensure that each module approximately achieves the overall mean within-degree, , we specify the following constraint: . If the sampled module sizes do not satisfy this criteria, the module sizes are re-sampled or an error is generated.
The between-degree sequence is generated by specifying db(vi)=d(vi)−dw(vi) for each node vi. To test if the between-degree sequence is realizable, we impose a criterion developed by Chungphaisan [33] (reviewed by Ivanyi [34]) for realizable degree sequences in multigraphs. To do so, we imagine a coarse graph, H, where the modules of G are the nodes of H (i.e. V(H)={C1,C2,…CK}), and the between-edges that connect modules of G are the edges of H. We note that H is a multigraph, because G allows multiple between-edges of G to connect each pair of modules. In this case, the degree sequence of H is .
The Chungphaisan criterion then specifies that the multigraph degree sequence {d(Ck)} on H is realizable if the following conditions are satisfied:
● Condition 1: the Handshake theorem is satisfied for {d(Ck)}: is even
● Condition 2: for (j=1,…,K−1).
Here, b is defined as the maximum number of edges allowed between a pair of nodes in H; in our case, b=max[ {db(vi)}], the maximum between-degree of any node vi∈G.
We also generate graphs with Q=0 by assuming the network is composed of a single module with no between-edges. Thus, dw(vi)=d(vi) and db(vi)=0 for all vi∈G.
Connecting edges
Based on the within-degree sequence and between-degree sequence specified above, edges are connected in two steps (Figure 1). Nodes that belong to different modules are connected based on their between-degree to form between-edges (Figure 1b) and nodes that belong to the same module are connected according to their within-degree to form within-edges (Figure 1c and 1d).
We connect between-edges using a modified version of the Havel-Hakimi algorithm. The Havel-Hakimi algorithm [35,36] constructs graphs by sorting nodes according to their degree and successively connecting nodes of highest degree with each other. After each step of connecting the highest degree node, the degree list is resorted and the process continues until all the edges on the graph are connected. Here, we modify this to construct between-edges by sorting nodes by highest between-degree, in order of highest total between-degree for the module to which they belong, and successively connecting the node at the top of the list randomly with other nodes. Connections are only made between nodes if they are not previously connected, belong to different modules, and do not both have within-degree of zero (to avoid disconnected components). After each step the between-degree list is resorted, and the process continues until all between-edges are connected. After all between-edges have been connected, the connections are randomized using a well-known method of rewiring through double-edge swaps [37]. Specifically, two randomly chosen between-edges (u,v) and (x,y) are removed, and replaced by two new edges (u,x) and (v,y), as long as u and x, and v and y belong to different modules, respectively. The swaps are constrained to avoid the formation of self loops and multi-edges. This process is repeated a large number of times to randomize edges.
We then connect within-edges using the standard Havel-Hakimi algorithm, applied to each module independently. Specifically, within-edges of a module are connected by sorting nodes of the module according to their within-degree and successively connecting nodes of highest within-degree with each other. Connections are only made between nodes if they are not previously connected, and do not both have a between-degree of zero (to avoid disconnected components). After each step the within-degree list is resorted and the process continues until all the within-edges of the module are connected. The connections are then randomized by rewiring through double-edge swaps [37]. We do not specify that each module be connected (only that the full graph is connected). However, if this is required, Taylor's algorithm can be used to rewire pairs of edges until the module is connected [38]. Specifically, the algorithm selects two random edges (u,v) and (x,y) that belong to two different disconnected components of the module. As long as (u,x) and (v,y) are not existing edges, the (u,v) and (x,y) edges are removed and (u,x) and (v,y) are added. Taylor's theorem proves that following such operation any disconnected module can be converted to a connected module with the same degree sequence.
Results and discussion
Using our simulation algorithm, we were able to generate modular random graphs of variable network size, number of communities, degree distribution, and community size distribution. In Figure 2, we show sample networks of varying levels of modularity, Q=0.1,0.3,0.6. We note that a network with three modules can approach a maximum modularity value of 2/3 (from equation 3), and thus Q = 0.6 is a relatively high modularity for this particular network type. In the sections that follow, we consider the algorithm performance, as well as structural properties of the generated graphs. We then highlight two applications of our model: 1) to generate benchmark graphs for validation of community detection algorithms and 2) to generate null graphs for the analysis of empirical networks. Community detection algorithms assist in identifying community structure in empirical networks. Our model is able to generate modular networks de novo to test these algorithms. Once community structure has been identified in an empirical network with a community detection algorithm, the number of communities and the modularity level (Q) (and, if desired, the community size distribution and within-degree sequence) can be used as input to our model to generate graphs that can act as random controls to test hypotheses about the empirical system.
Figure 2. Modular random graphs with n =150, m =375, K =3, P ( s =50)=1 andpk is power law with modularity values of: a) Q =0.1; b) Q = 0.3; and c) Q = 0.6. As the modularity increases, the ratio of the total number of edges within modules to the number of edges in the network increases (i.e. increases), while the remaining parameter values (degree distribution, network mean degree, number of modules) are held constant.
Performance & properties of generated graphs
Our model generates graphs that closely match the expected modularity and degree distribution. The deviation of the observed modularity is less than 0.01 from the expected value, given the specified partition. The modular random graphs with Poisson degree distribution generated by our model are similar to the ones described by Girvan and Newman [3] with linking (pin) and cross-linking probability (pout) equal to and respectively. However, our model overcomes several limitations of the model proposed by Girvan and Newman [3] and others [16,17] by considering heterogeneity in total degree, within-module degree distribution, and module sizes. Unlike many of the existing models [18-21], our model can generate modular random graphs with arbitrary degree distributions, including those obtained from empirical networks. Though we discuss modular random graphs with positive Q values, our model can also generate disassortative modular random graphs (see Figure S3 in Additional file 1). In this case, nodes tend to connect to nodes in other modules and thus the density of edge connections within a module is less than what is expected at random. Additionally, we also compare our model to graphs generated based on a degree-corrected stochastic block model (SBM). The details of the parameterization of the SBM and the results are shown in Figure S4 in Additional file 1).
Structural properties
There are several other topological properties (besides degree distribution and community structure) that can influence network function and dynamics. The most significant of these properties are degree assortativity (the correlation between a node's degree and its neighbor's degrees), clustering coefficient (the propensity of a node's neighborhood to also have edges among them) and average path length (the typical number of edges between pairs of nodes in the graph). We have developed this model to generate graphs with specified degree distribution and modularity, while minimizing structural byproducts. Thus, it is important to confirm that we have reached this goal with the generative model above.
To evaluate the status of other structural properties due to the generative model, we specify graphs of n=2000 following Poisson (λke−λ/k!), geometric (p(1−p)k−1), and power-law degree distributions with . We chose these particular types of degree distributions as they have widely studied in the context of biological networks [39-41]. Each network has K=10 modules and a module size distribution P(s=200)=1. We generate modular random graphs with these specifications and modularity values that range from Q=0 to Q=0.8, in steps of 0.1. For each level of modularity, we generated 50 such modular random graphs and calculated the degree assortativity (r), clustering coefficient (C), and average path length (L) for each network, which is illustrated in Figure 3. In networks with random community structure (Q=0), that is random graphs with specified degree distributions (such as those that would be generated by the configuration model [13]), the value of r,C, and L are what are expected at random. In Figure 3, we show that for increasing values of modularity, degree assortativity, clustering coefficient, and average path length remain relatively constant for all three network types (i.e. Poisson, geometric and power-law). At the highest levels of modularity, edge connections are constrained, particularly for the heavy-tailed geometric and power-law degree distributions, leading to an increase in clustering coefficient. Correlations between high clustering coefficient and high modularity have also been observed before [2]. The average path length for all network types also increases at the highest levels of modularity, likely reflecting the lack of many paths between modules, requiring additional steps to reach nodes in different modules. Thus, our model is able to increase levels of modularity in random graphs without altering other topological properties significantly.
Figure 3. Values of (a) Assortativity, r , (b) clustering coefficient, C , and (c) path length, L in modular random graphs do not vary significantly with increasing modularity ( Q ). Each graph has n=2000 nodes, a mean degree and K=10 modules with P(s=200)=1. The data points represent the average value of 50 random graphs. Standard deviations are plotted as error bars.
Biological networks show remarkable variation in network size, connectivity and community size distribution, with some of them having particularly small network size, high degree, and small module sizes (e.g. food-web networks). We therefore tested the performance of our generated networks under deviations in the network specifications of size, mean degree and module size distribution (results presented in Additional file 1: Figure S5, S6 and S7). We find that the structural properties of our generated modular random graphs remain constant, except for two constraining conditions: a) high average degree (10) and b) low average module size (50). At these parameter extremes, the modular random graphs become degree disassortative and have increased clustering coefficient. A similar observation of network degree disassortativity has been made in hierarchically modular networks [42]. In these two scenarios, the highest value of within-degree (dw(vi)) that a node can attain is constrained by the community size, which reduces the number of possible high within-degree nodes. As a consequence high within-degree nodes must connect to low within-degree nodes more than expected, resulting in a degree disassortative network. In these two cases, modules also become more dense and thus create more triangles resulting in a gradual increase in clustering. Path length, on the other hand, is not affected by these conditions and shows a consistent dependence on network size and mean degree, which is well known [43,44].
Application: benchmark graphs for community-detection algorithms
Detecting communities in empirical networks has been an area of intensive research in the past decade [45] since Girvan and Newman's seminal paper on community detection [3]. Extant techniques such as modularity maximization, hierarchical clustering, the clique-based method, the spin glass method etc. aim at achieving high levels of accuracy in detecting the correct partition (for a detailed review see [45]), but have their own set of strengths and weaknesses. Choosing the best algorithm can be a difficult task especially as algorithms often use distinct definitions of communities and perform well within that description. Thus, it is exceedingly important to test community-detection algorithms against a suitable benchmark. We propose our modular random graphs as benchmark graphs for the validation of existing and new algorithms of community detection.
To illustrate this use, we test the performance of six popular community detection algorithms: the Louvain method [46], fast modularity method [47], the spin-glass based method [48], the infoMAP method [49], label propagation [50] and the random-walk based method [51] using our modular random graphs as benchmarks. Specifically, we generate a modular random graph for each level of modularity and used these community detection algorithms to detect their community structure. We also test the performance of the algorithms on random graphs of specified degree distribution, with no modularity (i.e. Q = 0). Figure 4 summarizes the performance of these algorithms, as measured by the estimated Q, for modular random graphs with three different degree distributions (Poisson, geometric and power-law). We also investigated the robustness of these algorithms on replicate modular random graphs at each modularity level, with the results presented in (Additional file 1: Figures S8, S9 and S10).The Louvain, fast modularity algorithm, random-walk and infoMAP algorithm overestimate the modularity for networks with weak community structure, and underestimate the modularity for networks of moderate community structure across all three network types (Figure 4). Spinglass and label-propagation consistently underestimate the modularity of both weak and moderate community structure. All the algorithms are fairly accurate at the highest strengths of community structure across the various network types. The accuracy at a particular level of modularity and degree-distribution, however, varies for different algorithms. For instance, the performance of spin-glass algorithm is better for Poisson modular random graphs at modularity values of 0.5-0.6, whereas the Louvain and label-propagation algorithm out-perform on geometric random modular graphs at these modularity values.
Figure 4. Performance of the Louvain method [[46]], fast modularity method [[47]], the spin-glass based method [[48]], the infoMAP method [[49]], label propagation [[50]] and the random-walk based method [[51]] in networks with mean degree 10. Fill circles, open circles and triangles represent networks with Poisson, geometric and power-law degree distributions, respectively. Each data point represents the average over ten modular random graphs. Error bars represent standard deviations. The solid line is the reference line where estimated modularity is equal to the input modularity.
In addition to comparing the estimated values of modularity to the known values in the modular random graphs, we can compare the similarity in the partitions detected by the algorithms to the true partitions. For this comparison, we use the Jaccard similarity (J), which measures the similarity between two partitions based on the proportion of the union of the partitions that is made up by the intersection of the partitions [52]; as well as the Variation of Information (VI), which measures the distance between two partitions based on the amount of information lost when going from one partition to another [53]. These results are presented in the (Additional file 1: Figure S11). As reflected in the results above, we find that partitioning is inaccurate when the true community structure is weak but improves as the Qtrue value increases. These observations have also been noted before by Lacichinetti and Fortunato [54].
Application: null analysis of empirical networks
It is crucial to have random controls in the study of biological systems. Our algorithm can be used to generate null models and applied to the detection of structure in empirical biological networks. These null networks can be used to test hypotheses regarding the role of modularity and other topological features of the empirical networks. To do so, one would first determine the number of communities and modularity level (Q) of the sampled network using an appropriate community detection algorithm (the previous section describes the use of random modular graphs to validate existing algorithms of community detection). Our algorithm can then be used to generate an ensemble of networks that match the empirical degree structure and community structure, and then compare the structural, functional, or dynamical properties of the empirical network to those of the generated modular random graphs. Because our model generates graphs without any structural byproducts (as illustrated in a previous section), this is an appropriate model for generation of null models. We note that our algorithm does not necessarily require knowledge of the complete empirical network, but rather only estimates of the degree structure and community structure. The literature on algorithms for inference of network structure from a sample is growing, and currently includes work on inference of missing nodes, edges and even community structure [55-57].
We demonstrate this application using four classes of biological networks, namely: a) a food-web, representing the trophic interactions at Little Rock Lake in Wisconsin with a network size of 183 and average degree = 26.8 [58]; b) a protein-protein interaction network in Saccharomyces cerevisiae (a yeast) of size = 4713 and average degree = 6.3 [59]; c) a metabolic interaction network of Caenorhabditis elegans of size = 453 and average degree 9.0 [60]; and d) a network of social interactions in a community of dolphins living off Doubtful Sound, New Zealand of size = 62 and average degree = 5.1 [61]. Visualizations of the dolphin social interaction network and the food-web trophic interaction network and its modular random counterpart are shown in Figure 5.
Figure 5. Visualization of empirical and random graphs of social interaction of dolphins and food-web trophic interactions at the Little Rock Lake in Wisconsin. Figure (a) is the empirical network of Dolphin social network, (b) its modular random graph, and (c) its random graph counterpart with matched degree distribution (Q=0). Figure (d) is the empirical network for the food-web trophic interaction at Little Rock Lake in Wisconsin, (e) is its modular random graph and (f) its random graph counterpart with matched degree distribution. Modular random graphs have generated to match the overall degree distribution, network mean degree, the level of modularity and the number of modules of the empirical graphs. Random graphs with matched degree distribution are based on the configuration model.
For each of these four empirical networks, we generate modular random graphs (Figure 6, light gray bars) with three parameters estimated from the empirical networks: (a) the degree sequence, pk(b) the modularity, Q and (c) the average community size, . We note that as our goal is to construct null models, we assume that communities are of equal size, i.e. , and that the within-degree distribution matches the degree distribution fitted from the specified degree sequence (with estimated mean, ). (A second class of null models can be constructed with P(s) and the within-degree sequences estimated from the empirical networks, and we do this in Table S2 of Additional file 1). Specifically, we generate 25 such random graphs and measure structural properties of the generated graphs including clustering coefficient (C), average path length (L), degree assortativity (r).
Figure 6. Comparisons of empirical networks, modular random graphs and random graphs with matched degree distribution (based on the configuration model). The figure summarizes network statistics of the empirical network as well as the ensemble mean of two types of random graphs in terms of (a) Modularity, Q ; (b) Assortativity, r; (c) Path length, L and (d) Clustering coefficient, C. The path length value for the empirical Yeast-Protein interaction network is missing as the network contains disconnected components. Error bars denote standard deviation from the ensemble mean of the generated random graphs. Errors bars for modular random graphs in Figure 6(a) have been omitted as the value of modularity (Q) match the empirical networks perfectly. FW = Little Rock food web, YP = Yeast protein interaction network, CM =C.elegans metabolic network and DS = Dolphin social network.
We also generate random graphs based on the configuration model that have the same degree distribution and average network degree as the empirical network but are random with respect to other network properties for each of the four empirical networks (Figure 6, dark gray bars). Our modular random graph model identifies which network measures assume their empirical values in a particular network because of (i) the observed degrees and (ii) the latent community structure. The configuration model, on the other hand, only specifies (i) and not (ii) [13]. Comparison to these configuration model networks thus helps us highlight the utility of our model to identify which empirical patterns in a network are deserving of further investigation. Figure 6 shows the value of each of these properties for the empirical networks as well as the ensemble mean of modular random and random graphs with matched degree distribution.
From Figure 6 it is evident that none of the empirical biological networks have network structure identical to their null counterparts. This suggests that the structure of each of these biological systems is governed by more than what is specified by the degree distribution and community structure. However, the observed network properties of empirical networks are closer to the ensemble means of the modular random graphs, which indicates that modularity is an essential structural component of real biological networks and that it plays an important role in influencing other structural properties of the network. For instance, compartmentalization induced by modularity promotes species persistence and system robustness by containing localized perturbation [11,62,63], which might favor their selection during the course of evolution. Our results show that the empirical networks tested have a much higher modularity than the simple random graphs (Figure 6a) and therefore provide evidence for this selection. Out of the three network properties that we tested apart from modularity, we found clustering coefficient of the generated random graphs to be significantly different from each of the empirical counterparts. This may point to a functional role for "triangles" in these biological networks, significantly above or below what is prescribed by the degree and community structure.
Little Rock Lake food web interactions (FW)
Among the four empirical networks that we tested, the properties of the ensemble mean of null models such as assortativity and path length closely match most of the observed properties of Little Rock food web. The observed clustering coefficient of food web is strikingly lower than either of the random graphs which confirm the observations of low clustering in food web made by earlier studies (Figure 6d). The observed path length of this food web is short (Figure 6c) and only slightly longer than the path lengths of random graphs, which has also been noted before [64-66]. We note that for this food web, the structural properties of the random graphs with matched degree distribution are quite similar to those of modular random graph counterparts, suggesting that the degree distribution, particularly the high density of edges in the network governs most of the other topological characteristics of this network. Modularity, on the other hand, seems to play a minor role in dictating the structural properties of this network.
Yeast protein-protein interaction network (YP)
The empirical yeast protein network is more disassortative than the ensemble mean of null modular graphs (Figure 6b). Disassortative interactions in protein-protein interaction networks are known to reduce interferences between functional modules and thus increase the overall robustness of the network to deleterious perturbations [6], while also allowing for functions to be performed concurrently [67]. The results therefore suggest that disassortative interactions may be selected for in the evolution of biological networks. From Figure 6(d) it is also evident that the yeast protein network has a higher value of clustering coefficient than the expected value predicted by the modular random graphs. A high value of clustering coefficient indicates that there are several alternate interaction paths between two proteins, making the system more robust to perturbation [68].
C.elegans metabolic interaction network (CM)
The C.elegans metabolic network demonstrates a shorter path length but higher clustering coefficient than both modular and random graphs with matched degree distribution (Figure 6c and 6d). A high clustering coefficient and short path length suggests that the graph has small-world properties, which has been observed in other metabolic networks as well [69]. A highly disassortative degree structure is also well known in metabolic networks, although the mechanism leading to this property is unclear (see review by [39]). As the predicted value of disassortativity of the modular random graphs is closer to the observed value, our results suggest that the strong community structure of the metabolic networks could be one of the factors contributing to high degree disassortativity. (As discussed earlier, community structure leads to significant degree correlations in small networks with long-tailed degree distributions; see Figure S5 in Additional file 1 for an example).
Social interaction network of dolphins network at Doubtful Sound, New Zealand (DS)
The empirical social interaction network of dolphins that we investigated demonstrated a negative assortativity (or disassortativity) similar to other real biological networks (Figure 6b). Interestingly, the assortativity value of both null modular and random graphs with matched degree distribution counterparts of the dolphin network is lower than the observed value, which suggests that the network is more assortative than expected. Degree assortativity has also been observed in other animal [70] and human [4] social interaction networks. This result is quite intuitive for a social network and is also referred to as homophily: more gregarious individuals tend to interact with other gregarious individuals while introverted individuals prefer to associate with other introverts [14]. The empirical dolphin network also demonstrated a lower value of clustering coefficient than the expected values of either null model. Low clustering coupled with high degree assortativity indicates that dolphin populations may be more susceptible to the propagation of infection or information, as transmission may occur rapidly through the entire network with such properties [70,71].
In summary, the model that we propose in this study generates modular random graphs over a broad range of degree distribution and modularity values, as well as module size distributions. We highlight that our model is specifically designed to generate networks which have modularity evenly divided across its modules, modulo the impact of module size. This means that we are mitigating the resolution limit effect and indeed generating networks with the maximum modularity partition. We also confirm that structural properties of our generated modular graphs such as assortativity, clustering and path length remain unperturbed for a broad range of parameter values. This important feature allows these graphs to act as benchmark and control graphs to explicitly test hypotheses regarding the function and evolution of modularity in biological systems. Of the approaches available, our method provides flexibility and has been explored the most fully for these applications.
Compartmentalization of biological networks has been an area of great interest to biologists. What we refer to as community structure in this work is any segregation of a biological system into smaller subunits inter-connected by only a few connections. It has been suggested that modularity in a system promotes system robustness and enhances species persistence by containing localized perturbations [11,63]. Metabolic networks of organisms living in a variable environment have indeed been found to be more modular [62]. Maintaining and selecting for modularity in biological networks, however, comes at a great cost of reducing system complexity [72], longer developmental time and cost of complete module replacement in case of failure [73]. It is therefore unclear why modularity would be strongly selected for as a structural feature of biological systems. There is also a lack of evidence to prove that the functional localization of sub-goals overlaps with the structural segregation of the network into community structure. Our work provides a tool for the systematic study of network structure (through benchmark graphs) and of the impact of connectivity and compartmentalization on system function and dynamics (through control graphs).
The detection of community structure plays a crucial role in our topological understanding of complex networks. Currently the performance of community detection methods is usually evaluated based on ground-truth from real networks. However, determining reference communities in real networks is often a difficult task. Also, ground truth data on empirical network partitions do not necessarily identify system features based on network topology and thus may create a bias when analyzing community structure. A more convenient technique of evaluating community detection method is to use artificial random graphs, but has been limited as most of the models fail to incorporate degree heterogeneity of real networks. By providing a systematic method to generate benchmark graphs, our model can aid in the development of more robust community detection algorithms, and therefore improve our topological understanding of empirical networks.
A step beyond identifying the topological presence of network communities is the understanding of its evolution as well as the functional and dynamical role of community structure. We believe this process can be facilitated by using an appropriate class of control or null graphs. As a model for generating null networks, our method joins a suite of random graph models, each contributing to a hierarchy of null models. The simplest model for generating random graphs (based on only a single parameter) is the Erdős-Rényi random graph model, which produces graphs that are completely defined by their average degree and are random in all other respects. A slightly more complex and general model is one that generates graphs with a specified degree distribution (or degree sequence) but are random in all other respects [13,74,75]. These models can be extended to sequentially include additional independent structural constraints, such as degree distribution and clustering coefficient [2], or degree structure and community structure, as we have demonstrated here. A further extension to this work will be designing models that generate random graphs with multiple structural constraints. For example, our model can be combined with the one proposed by [2] to generate random graphs with specified degree distribution as well as tunable strength of modularity and clustering coefficient.
Availability and requirements
Project name: Modular random graph generatorProject home page:http://github.com/bansallab webciteOperating system(s): Platform independentProgramming language: Python 2.7Other requirements: Networkx Python packageLicense: BSD-styleAny restrictions to use by non-academics: None
Competing interests
The authors declare that they have no competing interests.
Authors' contributions
PS and SB contributed to algorithm design and implementation. PS, LOS, AC and SB contributed to manuscript writing. All authors read and approved the final manuscript.
This work was supported by NSF award DEB-1216054.
Proulx SR, Promislow DEL, Phillips PC: Network thinking in ecology and evolution.
Trends Ecol Evol 2005, 20(6):345-53. PubMed Abstract | Publisher Full Text
Bansal S, Khandelwal S, Meyers LA: Exploring biological network structure with clustered random networks.
BMC Bioinformatics 2009, 10:405. PubMed Abstract | BioMed Central Full Text | PubMed Central Full Text
Girvan M, Newman MEJ: Community structure in social and biological networks.
Proc Nat Acad Sci USA 2002, 99(12):7821-7826. PubMed Abstract | Publisher Full Text | PubMed Central Full Text
Newman M: Mixing patterns in networks.
Ravasz E, Somera AL, Oltvai ZN, Barabási AL, Mongru Da: Hierarchical organization of modularity in metabolic networks.
Science (New York, NY) 2002, 297(5586):1551-1555.
[http://www.ncbi.nlm.nih.gov/pubmed/12202830 webcite]Publisher Full Text
Maslov S, Sneppen K: Specificity and stability in topology of protein networks.
Science (New York, NY) 2002, 296(5569):910-913. Publisher Full Text
Han JDJ, Bertin N, Hao T, Goldberg DS, Berriz GF, Zhang LV, Dupuy D, Walhout AJM, Cusick ME, Roth FP, Vidal M: Evidence for dynamically organized modularity in the yeast protein-protein interaction network.
Nature 2004, 430(6995):88-93. PubMed Abstract | Publisher Full Text
Shen-Orr SS, Milo R, Mangan S, Alon U: Network motifs in the transcriptional regulation network of Escherichia coli.
Nature Genet 2002, 31:64-68. PubMed Abstract | Publisher Full Text
Krause AE, Mason DM, Ulanowicz RE, Taylor WW, Frank Ka: Compartments revealed in food-web structure.
Nature 2003, 426(6964):282-285. PubMed Abstract | Publisher Full Text
Stouffer DB, Sales-Pardo M, Newman MEJ, Guimerà R: Origin of compartmentalization in food webs.
Ecology 2010, 91(10):2941-2951. PubMed Abstract | Publisher Full Text
Olesen JM, Bascompte J, Dupont YL, Jordano P: The modularity of pollination networks.
Proc Nat Acad Sci USA 2007, 104(50):19891-19896. PubMed Abstract | Publisher Full Text | PubMed Central Full Text
Yang J, Leskovec J: Defining and evaluating network communities based on ground-truth. In Proc ACM SIGKDD Workshop Mining Data Semantics - MDS '12. New York: ACM Press; 2012:1-8.
Molloy M, Reed B: A critical point for random graphs with a given degree sequence.
Newman M: Assortative mixing in networks.
Phys Rev Lett 2002, 89(20):208701. PubMed Abstract | Publisher Full Text
Xulvi-Brunet R, Sokolov I: Reshuffling scale-free networks: from random to assortative.
Phys Rev E 2004, 70(6):066102.
[http://link.aps.org/doi/10.1103/PhysRevE.70.066102 webcite]
Lancichinetti A, Fortunato S, Radicchi F: Benchmark graphs for testing community detection algorithms.
Bagrow JP: Evaluating local community methods in networks.
Arenas A, Díaz-Guilera A, Pérez-Vicente C: Synchronization reveals topological scales in complex networks.
Phys Rev Lett 2006, 96(11):114102. PubMed Abstract | Publisher Full Text
Hintze A, Adami C: Modularity and anti-modularity in networks with arbitrary degree distribution.
Biol Direct 2010, 5:32. PubMed Abstract | BioMed Central Full Text | PubMed Central Full Text
Sawardecker EN, Sales-Pardo M, Nunes Amaral LA: Detection of node group membership in networks with group overlap.
Eur Phys J B 2008, 67(3):277-284.
[http://www.springerlink.com/index/10.1140/epjb/e2008-00418-0 webcite]
Sales-Pardo M, Nunes Amaral LA, Guimerà R: Module identification in bipartite and directed networks.
Phys Rev E, Stat Nonlinear Soft Matter Phys 2007, 76(3 Pt 2):036102.
Zhao H, Gao ZY: Modular effects on epidemic dynamics in small-world networks.
Euro Phys Lett (EPL) 2007, 79(3):38002. Publisher Full Text
Yan G, Fu ZQ, Ren J, Wang WX: Collective synchronization induced by epidemic dynamics on complex networks with communities.
Chu X, Guan J, Zhang Z, Zhou S: Epidemic spreading in weighted scale-free networks with community structure.
Salathe M, Jones JH: Dynamics and control of diseases in networks with community structure.
Clauset A, Shalizi CR, Newman MEJ: Power-law distributions in empirical data.
SIAM Rev 2009, 51(4):661-703. Publisher Full Text
Wang P, Robins G, Pattison P, Lazega E: Exponential random graph models for multilevel networks.
Soc Netw 2013, 35:96-115. Publisher Full Text
Chatterjee S, Diaconis P: Estimating and understanding exponential random graph models.
Ann Stat 2013, 41(5):2428-2461. Publisher Full Text
Karrer B, Newman M: Stochastic blockmodels and community structure in networks.
Newman MEJ: Detecting community structure in networks.
Good BH, de Montjoye YA, Clauset A: Performance of modularity maximization in practical contexts.
Zverovich IE, Zverovich VE: Contributions to the theory of graphic sequences.
Discrete Math 1992, 105:293-303. Publisher Full Text
Chungphaisan V: Conditions for sequences to be r_graphic.
Discrete Math 1974, 7:31-39. Publisher Full Text
Iványi A: Degree sequences of multigraphs.
Havel V: A remark on the existence of finite graphs.
Hakimi S: On realizability of a set of integers as degrees of the vertices of a linear graph. I.
J Soc Industrial Appl 1962, 10(3):496-506. Publisher Full Text
Gkantsidis C, Mihail M, Zegura E: The Markov chain simulation method for generating connected power law random graphs.
In Proceedings of the Fifth Workshop on Algorithm Engineering and Experiments Edited by Ladner RE. SIAM.
2003 2003:16–25
Taylor R: Constrained Switchings in Graphs. Berlin, Heidlberg: Springer; 1981.
Barabási AL, Oltvai ZN: Network biology: understanding the cell's functional organization.
Nat Rev Genet 2004, 5(2):101-113. PubMed Abstract | Publisher Full Text
Przulj N: Biological network comparison using graphlet degree distribution.
Bioinformatics 2007, 23(2):e177-e183. PubMed Abstract | Publisher Full Text
Tanaka R: Scale-rich metabolic networks.
Phys Rev Lett 2005, 94(16):168101. PubMed Abstract | Publisher Full Text
Jing Z, Lin T, Hong Y, Jian-Hua L: The effects of degree correlations on network topologies and robustness.
Dorogovtsev S, Mendes J, Oliveira J: Degree-dependent intervertex separation in complex networks.
Hołyst J, Sienkiewicz J, Fronczak A, Fronczak P, Suchecki K: Universal scaling of distances in complex networks.
Newman MEJ: Communities, modules and large-scale structure in networks.
Nat Phys 2011, 8:25-31. Publisher Full Text
Blondel VD, Guillaume JL, Lambiotte R, Lefebvre E: Fast unfolding of communities in large networks.
J Stat Mech Theory Exper 2008, 2008(10):P10008. Publisher Full Text
Clauset A, Newman M, Moore C: Finding community structure in very large networks.
Reichardt J, Bornholdt S: Statistical mechanics of community detection.
Rosvall M, Axelsson D, Bergstrom CT: The map equation.
Raghavan U, Albert R, Kumara S: Near linear time algorithm to detect community structures in large-scale networks.
Phys Rev E 2007, 76(3):036106.
[http://link.aps.org/doi/10.1103/PhysRevE.76.036106 webcite]
Pons P, Latapy M: Computing communities in large networks using random walks.
J Graph Algorithms Appl 2006, 10(2):191-218. Publisher Full Text
Downton M, Brennan T: Comparing classifications: an evaluation of several coefficients of partition agreement.
Meilǎ M: Comparing clusterings by the variation of information.
Learn Theory Kernel Mach 2003, 2777:173-187. Publisher Full Text
Lancichinetti A, Fortunato S: Community detection algorithms: a comparative analysis.
Chen J, Zaïane O, Goebel R: Local community identification in social networks.
Kim M, Leskovec J: The network completion problem: inferring missing nodes and edges in networks.
Lin W, Kong X, Yu PS, Wu Q, Jia Y, Li C: Community detection in incomplete information networks. In Proc 21st Int Conf World Wide Web - WWW '12. New York: ACM Press; 2012:341-341.
Martinez N: Artifacts or attributes? Effects of resolution on the Little Rock Lake food web.
Ecol Monograph 1991, 61(4):367-392. Publisher Full Text
Colizza V, Flammini A, Maritan A, Vespignani A: Characterization and modeling of pro-tein-protein interaction networks.
Phys A Stat Mech Appl 2005, 352:1-27. Publisher Full Text
Jeong H, Tombor B, Albert R, Oltvai ZN, Barabási aL: The large-scale organization of metabolic networks.
Nature 2000, 407(6804):651-654. PubMed Abstract | Publisher Full Text
Lusseau D, Schneider K, Boisseau OJ, Haase P, Slooten E, Dawson SM: The bottlenose dolphin community of Doubtful Sound features a large proportion of long-lasting associations.
Behav Ecol Sociobiol 2003, 54(4):396-405. Publisher Full Text
Parter M, Kashtan N, Alon U: Environmental variability and modularity of bacterial metabolic networks.
BMC Evol Biol 2007, 7:169. PubMed Abstract | BioMed Central Full Text | PubMed Central Full Text
Stouffer DB, Bascompte J: Compartmentalization increases food-web persistence.
Proc Nat Acad Sci USA 2011, 108(9):3648-3652. PubMed Abstract | Publisher Full Text | PubMed Central Full Text
Williams RJ, Berlow EL, Barabási AL, Martinez ND, Dunne Ja: Two degrees of separation in complex food webs.
Proc Nat Acad Sci USA 2002, 99(20):12913-12916. PubMed Abstract | Publisher Full Text | PubMed Central Full Text
Montoya JM, Sole RV: Small world patterns in food webs.
J Theor Biol 2002, 214(3):405-412. PubMed Abstract | Publisher Full Text
Williams RJ, Martinez ND, Dunne Ja: Food-web structure and network theory: the role of connectance and size.
Proc Nat Acad Sci USA 2002, 99(20):12917-12922. PubMed Abstract | Publisher Full Text | PubMed Central Full Text
Khor S: Concurrency and network disassortativity.
Artif Life 2010, 16(3):225-232. PubMed Abstract | Publisher Full Text
Wuchty S, Barabási AL, Ferdig MT: Stable evolutionary signal in a yeast protein interaction network.
BMC Evol Biol 2006, 6:8. PubMed Abstract | BioMed Central Full Text | PubMed Central Full Text
Wagner A, Fell DA: The small world inside large metabolic networks.
Proc Biol Sci R Soc 2001, 268(1478):1803-1810. Publisher Full Text
Croft D, James R, Ward AJW, Botham MS, Mawdsley D, Krause J: Assortaive interactions and social networks in fish.
Oecologia 2005, 143:211-219. PubMed Abstract | Publisher Full Text
Newman M: Properties of highly clustered networks.
Welch JJ, Waxman D: Modularity and the cost of complexity.
Evol Int J Organic Evol 2003, 57(8):1723-1734. Publisher Full Text
Krohs U: The cost of modularity. In Functions in Biological and Artificial Worlds: Comparative Philosophical Perspectives. MIT Press; 2009:259-276.
Aiello W, Chung F, Lu L: A random graph model for massive graphs. In Proc Thirty-Second Annual ACM Symposium on Theory of Computing - STOC '00. New York: ACM Press; 2000:171-180.
Newman MEJ, Strogatz SH, Watts DJ: Random graphs with arbitrary degree distributions and their applications.


text:
- Education
- Admissions
- Campus Offices
- Certificates
- Continuing Medical Education
- Degree Programs
- Departments
- Education Resources
- Indians Into Medicine
- Interprofessional Education
- Library
- Seven Generations Center of Excellence in Native Behavioral Health
- Residency Programs
- Research
- Areas of Research
- Facilities/Cores
- Grant Resources
- Research Experience for Medical Students (REMS)
- Research Centers
- Centers
- Clinical Centers
- Service Centers
- Center for Rural Health
- Fetal Alcohol Syndrome Center
- Mobile Simulation (SIM-ND)
- National Indigenous Elder Justice Initiative
- National Resource Center on Native American Aging
- North Dakota Area Health Education Center (AHEC)
- North Dakota Tobacco Quitline
- Rural Assistance Center (RAC)
- Rural Surgery Support Program
- Simulation Center (ND STAR)
- Faculty/Staff
- Administration
- New Building
- About Us
Anatomy DegreesFinancial Aid Courses Facilities Deeded Body Program Mission Statement Faculty/Staff Contact
Anatomy and Cell Biology
Welcome to the homepage of the Department of Anatomy and Cell Biology. Our department is a unit of the UND School of Medicine and Health Sciences and is housed in the Edwin C. James Medical Research Facility.
The Department of Anatomy and Cell Biology offers graduate programs leading to the MS, PhD, and MD/PhD degrees.
Please follow the links on the left to find out more about our department and feel free to contact us if you have any questions.

subset: commoncrawl


text:
The law schools aren't happy about that rule and, truth to tell, I'm not crazy about it, either. But I'm not about to boycott the armed forces of the United States on account of that policy. Because I owe them too much. Like loyalty and gratitude and respect. And a decent welcome when they drop by to make their case. Don't all Americans owe the military that much, even those who teach law?
It didn't take the chief justice long to shoot down the law schools' argument that they were being forced to agree with the military's policy. After all, the court requires high schools to allow equal access for religious clubs without any danger of making those schools endorse religion. "We have held," wrote the chief justice, "that high school students can appreciate the difference between speech a school sponsors and speech the school permits because legally required to do so . . . . Surely students have not lost that ability by the time they get to law school."
Well, maybe they have in the higher reaches of academe. Or so these distinguished law schools were reduced to arguing. To borrow an observation from George Orwell that never seems to lose its relevance: "One has to belong to the intelligentsia to believe things like that: No ordinary man could be such a fool."
Naturally the law schools aren't happy with how this fight they picked came out. To quote Chai Feldblum, a professor of law at Georgetown, this decision should serve as a "call to arms" to the schools. One trusts she was speaking only metaphorically. If not, there's still a bright side: Professor Feldblum could yet come to see the utility of military training for lawyers.
The court's decision in Rumsfeld may have lacked the surprise factor that makes for Big News, but it offers real hope. For you'd think at least one of the justices would have fallen for the law schools' involved argument that to deny them federal aid merely because they wanted to snub the military would be an unconstitutional infringement on their freedom of speech, their need for diversity on campus, their sacred conscience and general grabbiness, etc. But not even one justice swallowed the law schools' tangled line.
Whatever this decision may say about the Constitution, it says something most assuring about the court itself. Can the fog in Washington be lifting? Have reports of the death of common sense in the law been greatly exaggerated? Keep the good thought.
Pulitzer Prize-winning Paul Greenberg, one of the most respected and honored commentators in America, is the editorial page editor of the Arkansas Democrat-Gazette.
Democrats Remain Silent as Obama Economy Kills Jobs, Freezes Wages Amid More Layoffs to Come | Donald Lambro
For it before she was against it: Hillarybot flip-flops on TPP after praising it repeatedly until recently | Allahpundit


text:
Max guests: 6
District: Observatoire
Nearest station: Montparnasse - Edgar Quinet
Minimum stay: 1 night
This elegant apartment building is located in a lively district surrounded by French bistros, cafes and shops. Nearby there are some of the best cinemas in Paris, a wonderful food market and the famous Coupole Brasserie. One of the most charming areas of Paris, Saint-Germain-des-Près is just a 10 minutes walk from your door. Here you will find shopping, restaurants and one of Paris' largest parks, the beautiful Luxembourg Gardens. Metro / subway stations as well as other means of public transportation are conveniently located nearby.
This location offers studios, one bedroom with den and spacious two bedroom apartments. All suites are completely refurbished and beautifully appointed. Large windows, parquet flooring and tasteful, contemporary furnishings lend a light and modern feel to this delightful Parisian, period style building.
Apartment Information
- Fully Equipped Kitchen with Washer / Dryer & Microwave
- Colour TV (Cable TV from €20)
- Direct Dial Telephone
- Music System
- Air-Conditioning
- Internet Access
Building Features
- 10 Apartments
- Key Code Door Entry System
- House Manager / Reception (not resident)
- Weekly Maid Service & Linen Change
- Lift
- Dry Cleaning / Laundry Service (chargeable)
|Apartment Size
|Maximum Number of Guests
|Nightly Rates valid until 31 December 2014
|Length of Stay
|1 - 7 Nights
|8 - 28 Nights
|29+ Nights
|One Bedroom
|2 - 4
|Two Bedroom (two guests using sofa bed)
|4 - 6
|Note: Rates are inclusive of Local Taxes. Discounts are available for longer stays.
How do I book?
- Once you have chosen from our selection of apartments, click the "Book securely online!" or if you prefer to book by fax, click "Book by fax!" button above to go to the relevant booking form.
- After you complete and send your reservation request (by secure online booking or fax), we check the availability and immediately reserve your apartment.
- A confirmation is sent to you by email and/or fax within 24 hours - that's it !
- If your 1st or 2nd choice apartments are not available we will let you know with details of a suggested apartment.
- Please read both the terms and conditions of this apartment and our general deposit and booking terms
Nearby events & exhibitions...
Tintin and Snowy arrive at the Musée en Herbe! exhibition (1.4 miles away)
Date: Thursday 12th February 2015 - Thu 31st Dec 2015
Venue: Musée en herbe
Blistering barnacles, it's Tintin!In 2015, to mark the 40th anniversary of the Musée en Herbe, Tintin has set down his suitcase in Paris, after 7 years of traveling! The treasures of Hergé will be is display, enriched by works from museums and galleries. Visitors will discover an ...
Full details
UEFA EURO 2016 (1.4 miles away)
Date: Friday 10th June 2016 - Sun 10th Jul 2016
Venue: Different cities around France
From 10 June to 10 July 2016, France will host the final round of the 15th UEFA European Football Championships. A sporting event that the country knows well as it will be the organizer for the 3rd time in less than 60 years. For the first time since 1960 (the year in which this European ...
Full details
BNP Paribas Masters (2.5 miles away)
Date: Saturday 31st October 2015 - Sun 8th Nov 2015
Venue: Palais Omnisports de Paris-Bercy
After Roland Garros, BNP Paribas Master is the next most important French tennis tournament. The last stage on the Masters route for the top 8 players, this tournament allows the players still in with a chance to confirm their place at the Masters final, promising some spectacular matches. ...
Full details
Paris Comic Con (4 miles away)
Date: Friday 23rd October 2015 - Sun 25th Oct 2015
Venue: The Grande halle de la Villette
Comic Con Paris, the festival of imaginary cultures, is the key European event for fans of comics, fantasy, fantasy and science fiction! For its new edition, Comic Con will take place from 23 to 25 October 2015 at the Grande Halle de la Villette.
Full details
Favourite apartmentsSorry, you do not appear to have cookies enabled, without which the favourites feature will not work. How to enable cookies.
Featured Apartment
Bridge Street Residences
Fully equipped kitchen including dishwasher, microwave... Bathroom with washer machine Direct telephone line / TV with DVD/ Hi-Fi syst...
Read more...


text:
Download mmNote iPhone iPad iOS
mmNote is a simple, easy-to-use notepad application for iPhone and iPod touch. It can keep many memos in hierarchical structure and it has quick search function, so user can create, store, refer to and edit many memos swiftly.
mmNote also provides synchronizing function with MacNote3 (Macintosh notepad application) via Wifi. User can export those memos to their own Macintosh (with its images), also can create and edit memos on Mac and export them to iPhone/iPod touch. Via this function, longer memo can be stored in the iPhone/iPod touch easily.
Click4more: Related apps mmnote
The mmNote is now available as a free download on Apple Store for both iPhone and iPad owners.The application is designed for use in English language. It weighs in at only 0.4 MB to download. It is highly advisable to have the latest app version installed so that you don`t miss out on the fresh new features and improvements. The current app version 3.0.0 has been released on 2014-11-08. The Apple Store includes a very useful feature that will check if your device and iOS version are both compatible with the app. Most iPhone and iPad are compatible. Here is the app`s compatibility information: Compatible with iPhone, iPod touch, and iPad. Requires iOS 3.2 or later
More Info: Find more info about mmNote in sekn`s Official Website : http://homepage.mac.com/nsekine/SYW/SYWSoft/softOSXE.html
iOS mmNote 3.0.0 Mobile
More in Business - for mmNote iPhone
More by sekn - for mmNote app ioS


text:
All Android applications categories
Need an anti dog app with different cat sounds? Try Cat Sounds. Have you ever heard a cat cry? or yell? Guess which sound it is..A must have for cat lovers. Try as well FarmAnimals and SeaAnimals, for free on the Android Market.
from 3.103 reviews


text:
Sort by: Date or Title
Some Experiences of an Irish R.M., [en] 1903
All on the Irish Shore
Irish Sketches, [en] 1903
See it as donating a moment of your social media time, every little thing helps us improve and stay online.
When the economic downturn ends Matty Cruzs co... Read more
Cara Devon has always suffered curiosity and im... Read more
A telekinetic teenager. A telepathic child. A p... Read more
A century after an apocalyptic war reduces all... Read more
Fall in love with the Kensington siblings in th... Read more


text:
Kiene Dental Group 913-631-5622
Visit website 11005 W. 60th Street, Suite 240, Shawnee, KS 66203 Opens today at 7 a.m.
Products / Temporomandibular Joint Disorder (TMJ)
The jaw joints, or temporomandibular (TM) joints, are in front of each ear and connect the lower jawbone (mandible) to the skull. These flexible joints allow jaw movement that helps with talking, chewing, swallowing, and other functions. Many people may have pain or discomfort in and around the jaw joints during their lives. This pain and discomfort in the jaw muscles and joint is called temporomandibular disorder (TM disorder).
To read more about this disorder, please follow the link below to our website.


text:
Book your room at Enjoying International Hotel
Standard Room, 2 Single BedsMax Occupancy: 3 guests (up to 1 child, 1 infant)
Business Single Room, 1 King BedMax Occupancy: 3 guests (up to 1 child, 1 infant)
Deluxe RoomMax Occupancy: 3 guests (up to 1 child, 1 infant)
Standard Room, 2 Single Beds (Deluxe)Max Occupancy: 3 guests (up to 1 child, 1 infant)
Executive SuiteMax Occupancy: 3 guests (up to 1 child, 1 infant)
Standard Duplex, 2 Single Beds (Suite)Max Occupancy: 3 guests (up to 1 child, 1 infant)
Get an overview of this hotelKunming hotel in Kunming City Centre with full-service spa and restaurant
Located in Kunming City Centre, this hotel is within 2 mi (3 km) of East Pagoda, Tuodong Stadium, and West Pagoda. Yunnan Provincial Museum and Yuantong Si are also within 3 mi (5 km).
Hotel Features
A full-service spa, a restaurant, and a nightclub are available at this hotel. Free WiFi in public areas and free self parking are also provided. Other amenities include a bar/lounge, a sauna, and a business center.
Room Amenities
Rooms offer hair dryers.Information missing or incorrect? Tell us!
Hotel Amenities
Hotel Amenities
Enjoying International Hotel features a full-service spa and a sauna. The hotel offers a restaurant. A bar/lounge is on site where guests can unwind with a drink. High-speed wireless Internet access is complimentary.
Business-related amenities consist of a business center and meeting rooms. This business-friendly hotel also offers a nightclub, an arcade/game room, and concierge services. Complimentary self parking is available on site.
- Arcade/game room
- Bar/lounge
- Business center
- Concierge services
- Elevator/lift
- Full-service spa
- Grocery/convenience store
- Free WiFi
- Meeting rooms
- Nightclub
- Luggage storage
- Restaurant
- Safe-deposit box at front desk
- Free self parking
- Sauna
- Wedding services
Family Friendly Amenities
- Free Wi-Fi
- Grocery/convenience store
- Arcade/game room
Available in some public areas: Free WiFi
Free self parking
Room Amenities
- Hair dryer (on request)
Where to Eat
Enjoying International Hotel has a restaurant on site.
Spa Services
Guests can indulge in a pampering treatment at the hotel's full-service spa. Services include massages.
- Massages
Hotel Policies
Payment types
You need to know
Extra-person charges may apply and vary depending on hotel policy.
Government-issued photo identification and a credit card or cash deposit are required at check-in for incidental charges.
Special requests are subject to availability upon check-in and may incur additional charges. Special requests cannot be guaranteed.


text:
Rock / Alternative / Rock
Manhattan, NY
Time Will Tell Pro
Pop Punk / Pop / Alternative
S Plainfield, NJ
Rock / Alternative / Rock
Lakeview, NY
Rock / Other
Las Vegas, NV
Green Day Pro
Rock / Punk / Alternative
Aptos, CA
Your comment is being submitted, please wait a moment.
abbiamo caricato un po' di nuove tracce sul nostro profilo!! Nov 18
Hi! I'm Eric from a Phoenix Rocktronic band called LIA! I am 99% sure you will like us! http://www.purevolume.com/lostinatlantis I suggest "Alien" because it's super epic! But, "Ready To Go" and "Tek No" are good too! And they are up for free download! Let me know what you think! :) Oct 01
please have a listen to my band, Anek: http://www.purevolume.com/anek May 06


text:
7:00 PM Boys Varsity Football
7:00 PM - 9:00 PM HEA Scholarship Play Performance
7:00 PM Girls Varsity Field Hockey
3:45 PM Girls Varsity Soccer
4:00 PM - 5:00 PM Curriculum Council Meeting
5:00 PM - 6:00 PM School Board General Services Committee Meeting
7:00 PM Boys Varsity Soccer
7:00 PM Girls Varsity Volleyball
7:00 PM - 9:00 PM School Board Meeting
8:00 AM - 11:30 AM PSAT Testing
9:00 AM - 9:30 AM HMS BAT Meeting
9:30 AM - 10:30 AM HMS PTO Meeting
7:30 PM Girls Varsity Field Hockey
5:00 PM Girls Varsity Volleyball
The Hershey Education Association will present its 39th Scholarship Production on "The Adventures of Rikki Tikki Tavi" an adaptation of a short story by Rudyard Kipling in The Jungle Book. The play will feature teachers and staff members from across the district and promises to be a fun, family-friendly time. Best of all, proceeds from the production go to a scholarship fund that benefits Hershey students attending college. There will be two showings, one each on Friday, October 9 and Saturday 10. Both shows will be presented in the Hershey High School Auditorium; the curtain rises at 7 p.m. Tickets will be sold at the door for $5.
Monday, October 12 is an ins-service day for teachers. There will be no classes for students. School building offices will be closed until 1 p.m. to facilitate staff training; the District Office will be open normal business hours. The regular school schedule will resume Tuesday, October 13.
Join the Youth Alliance, former Harlem Globetrotter Seth Franco and DTSD in addressing a serious subject. Bullying is everybody's problem—victim, perpetrator, and bystander. Let's address this issue from each standpoint so that students are equipped to handle negative situations and create a healthier overall environment. This Family Nigh event will be Thursday, October 15 beginning at 6:30 p.m. at Hershey High School.
DTSD is now offering its "2015-16 All-Sports Pass" to DTSD students and district residents. The pass allows the bearer to attend all home regular season sporting events during the 2015-16 school year at no additional cost. All-sports passes can be purchased in the Athletic Office located in Hershey High School at a cost of $20 for students and $40 for adults.


text:
Royalty Free Music Unique To Your Project - Every Time
Royalty Free Music — Unique To Your Project – Every Time
Try SmartSound's Award Winning and Patented Technology Yourself
New Royalty Free Music Search
Or Browse By (Click to add multiple browse filters)
Genre | Instrument | Keyword | Advanced
Royalty Free Music Search Results (You are in TRACK VIEW. Switch to ALBUM VIEW)
The following tracks match: Atmospheric, Serene, Drama
VistasA cerebral, refined piece of smooth jazz, with warm guitars adding complexity. Great for creating a smooth sophisticated atmosphere.https://www.smartsound.com/strata/images/BS22AD_200.jpgSingle56009-ST$ 39.9556009-EX$ 69.9556009-W$ 149.95Keywords: Sleek, Atmospheric, Ethereal, Gentle, Mystical, Reflective, Relaxed, Serene, Ambient, Drama, Mellow, Quiet, Soft Genre: New Age, Easy-Listening/New Age Production Types: TV/ Film Drama, Documentary, Action-Drama, Meditation, Science, Spoken Word/Narration, Background Instrument: Electronic, Instrumental
Vistas from the album Ambient Drama
Morning AfterA slow build to majestic, this uplifting piece aids in showing the ever-growing and everlasting love between two people, perfect for that final romantic scene.https://www.smartsound.com/filmscore/images/FSCSG01_200.jpgSingle68510-ST$ 39.9568510-EX$ 69.9568510-W$ 149.95Keywords: Atmospheric, Dramatic, Melancholy, Reflective, Serene, Tender, Touching, Tranquil, Ambient, Drama, Emotional, Poignant Genre: Romantic, Orchestral, New Age Production Types: TV/ Film Drama, Commercials, Documentary, Indie Film Instrument: Orchestra, Guitar (Acoustic), Piano, New Age Ensemble, Acoustic, Instrumental, Guitar
Morning After from the album Craig Stuart Garfinkle Vol 1 - Emotive & Dramatic
MovingThis introspective and sparse work is great for thoughtful moments in Indie projects.https://www.smartsound.com/strata/images/STRATSUP_200.jpgSingle67106-ST$ 39.9567106-EX$ 69.9567106-W$ 149.95Keywords: Atmospheric, Calm, Delicate, Ethereal, Gentle, Innocent, Relaxed, Serene, Sparse, Tranquil, Drama, Mellow, Quiet, Soft Genre: Ballad, Lyrical, Minimal, Indie, Specialty Production Types: TV/ Film Drama, Indie Film, Short Film, Action-Drama, Biography, Spoken Word/Narration, Background Instrument: Piano, Acoustic, Instrumental
Moving from the album Subtle Progression
Dreaming For AnswersA introspective work for piano and orchestra.https://www.smartsound.com/strata/images/STRATNB_200.jpgSingle65202-ST$ 39.9565202-EX$ 69.9565202-W$ 149.95Keywords: Atmospheric, Dramatic, Light, Reflective, Serene, Drama, Quiet, Soft Genre: Orchestral, Indie Production Types: Documentary, Indie Film, Short Film, Action-Drama, Spoken Word/Narration, Background Instrument: Orchestra, Piano, Acoustic, Instrumental
Dreaming For Answers from the album Narration Backgrounds
8FoldEthereal, sparse and introspective guitar work, ideal for thought provoking scenes in your next indie film. Includes floating vocals.https://www.smartsound.com/strata/images/STRATLA_200.jpgSingle59501-ST$ 39.9559501-EX$ 69.9559501-W$ 149.95Keywords: Atmospheric, Calm, Ethereal, Gentle, Hypnotic, Pensive, Serene, Solemn, Subdued, Ambient, Drama, Mellow, Quiet, Soft Genre: Ballad, Indie, Specialty Production Types: Indie Film, Short Film, Action-Drama, Meditation, Science, Background Instrument: Guitar (Acoustic), Instrumental, Guitar
8Fold from the album Lighter Than Air
Night LightA spacious piano work, full of mystery and mood-setting etherealness. Distant drums keep the pulse.https://www.smartsound.com/strata/images/STRATLA_200.jpgSingle59507-ST$ 39.9559507-EX$ 69.9559507-W$ 149.95Keywords: Atmospheric, Calm, Dramatic, Ethereal, Serene, Subdued, Ambient, Drama, Abstract, Quiet, Soft Genre: Downtempo, Indie, Trip Hop, Electronic Production Types: Indie Film, Short Film, Action-Drama, Science, Background Instrument: Piano, Instrumental
Night Light from the album Lighter Than Air
Time To GoA compassionate and ethereal slice of acoustic pop rock. The competition is over for one person, and it's time to reflect on an amazing journey.https://www.smartsound.com/strata/images/BS16RC_200.jpgSingle55210-ST$ 39.9555210-EX$ 69.9555210-W$ 149.95Keywords: Atmospheric, Hypnotic, Melancholy, Pulsating, Serene, Subdued, Drama Genre: Specialty Production Types: TV/ Film Drama, Reality TV, Action-Drama, Background Instrument: Studio Orchestra, Strings, Instrumental
Time To Go from the album Reality Contest
Subdued Suspense AAt the center of this churning spiral of synths and clever percussion is an enchanting piano theme that will lure in your audience immediately. Great for suspense with a emotional undercurrent.https://www.smartsound.com/strata/images/strata_cover_100.jpgSingle50613-ST$ 39.9550613-EX$ 69.9550613-W$ 149.95Keywords: Atmospheric, Dramatic, Ethereal, Haunting, Mystical, Serene, Subdued, Suspenseful, Drama, Investigative Genre: Themes, Orchestral Production Types: TV/ Film Drama, Suspense, Action-Drama Instrument: Studio Orchestra, Instrumental
Subdued Suspense A from the album Edgy Drama TV
DistancesA rolling, emotional piano piece, geared for moments of contemplation or dramatic turns of events.https://www.smartsound.com/producer/images/PS53_200.jpgSingle9603-ST$ 39.959603-EX$ 69.959603-W$ 149.95Keywords: Atmospheric, Dramatic, Hypnotic, Pensive, Serene, Drama, Mellow, Emotional, Poignant, Simple Genre: Minimalism, Indie, Classical Production Types: Documentary, Indie Film, Short Film, Action-Drama, Meditation, Tribute/Memorial, Background Instrument: Solo, Piano, Acoustic, Instrumental
Distances from the album Piano Portraits (PS53)
The following tracks match: Atmospheric, Drama
Mirror Of DreamsA mysterious intro with an intense, heavy-bottomed synth-bass explodes into a soaring piano-synth hook creating an uplifting melody rising above all else with emotion and hope.https://www.smartsound.com/artist/images/ASFB02_200.jpgSingle70607-ST$ 39.9570607-EX$ 69.9570607-W$ 149.95Keywords: Sleek, Cool, Uplifting, Atmospheric, Intense, Powerful, Ambient, Drama, Hopeful Genre: Club, Electronica, Urban, Dubstep, Pop Production Types: Commercials, Background Instrument: Electronic, Piano, Synthesizer, Instrumental
Mirror Of Dreams from the album Ultra Pop
Choose your license:
|Customizable with Sonicfire Pro and Quicktracks
|Personal and professional use
|Promote a product or service
|Use on my own website
|Videos created for a third party
|Use on my clients website
|Monetized videos on YouTube, Vimeo, Facebook, Etc.
|Display at Film Festivals
|Display in theaters
(one theater)
(unlimited theaters in one country)
|Assign Distribution Rights
|DVDs & Downloads
(up to 2000)
(up to 10000)
|In mobile apps
|Local TV/radio broadcasting (includes advertising)
|National TV/radio broadcasting (includes advertising)


text:
Archive for Friday, August 27, 2010
Tonganoxie police calls, Aug. 26, 2010
August 27, 2010
Tonganoxie police calls filed Aug. 26, 2010:
• Unknown 911 call, 1:11 p.m. in the 600 block of East Fourth Street.
• Fire call, 6:10 p.m. in the 100 block of West Eighth Street.
• Suspicious activity, 8:54 p.m. in the 400 block of Stonecreek Drive.
• Suspicious activity, 10:34 p.m. in the 500 block of Northstar Court.
More like this story
- 3 suspects in custody after high-speed police chase ends in Lawrence
- Police: Woman arrested in battery of police horse in Wichita
- Suspect in homicide case takes authorities on vehicle chase that ends in Basehor
- Tonganoxie man arrested on suspicion of child endangerment, alcohol charges
- Bond increase for Kansas man charged with molestation
Use the comment form below to begin a discussion about this content.
Commenting has been disabled for this item.


text:
Meghan McCain: Christine O'Donnell Seen as a Nutjob
**Written by Doug Powers
Disregard the above photo. I'm only putting it there to remind myself to check my tire pressure later this afternoon.
ABC billed their "This Week" program this morning as featuring "four powerhouse guests." One of those four "powerhouse guests" was John McCain's supergenius daughter (if it rains today it's because David Brinkley is up there weeping at what his show has become), who offered some powerhouse insights on the Delaware Senate election:
Meghan McCain, author of the book "Dirty Sexy Politics," said Christine O'Donnell, the Republican candidate for Senate in Delaware, was real trouble.
"Well, I speak as a 26-year-old woman and my problem is that, no matter what, Christine O'Donnell is making a mockery of running for public office," McCain told anchor Christiane Amanpour. "She has no real history, no real success in any kind of business."
In that case, O'Donnell should forget about the Senate and run for president.
Maybe I'm just in a grumpy mood, but it's annoying when people have to state their own age and sex to remind listeners who they represent. "I speak as a 26 year old woman…" Well no kidding! Actually I think Meghan McCain speaks as a 17 year old valley girl, but what do I know?
McCain also believes that political inexperience is dangerous to the nation, but since many of our problems have been caused by entrenched experienced politicians, take this, like almost everything else she says, with a grain of salt:
McCain, daughter of Sen. John McCain, R-Ariz., said that the message, "that sends to my generation is: one day you can just wake and run for Senate, no matter how [much of] a lack of experience you have. And it scares for me for a lot of reasons."
"I just know, in my group of friends, it turns people off because she's seen as a nutjob," she said.
Anybody can run for political office, and I thought that was a good thing because it was intended to keep the elites from having an unbreakable grip on power, occasionally resulting in dingy kids with unmerited Sunday morning talk show clout. That's not the kind of progressive, open-minded "just way left of right-of-center" thinking on which Meghan McCain claims to pride herself.
In any case, that "nutjob" is out raising Harry Reid's pet by a two to one margin.
Did I just waste time talking about what Meghan McCain said? Sorry about that — time to go watch football now!
**Written by Doug Powers
Twitter @ThePowersThatBe
The Sundance Kidder: Global warming alarmist Robert Redford says deniers are 'afraid of change'
September 18, 2015 01:46 PM by Doug Powers
Thursday open thread: Hillary talks gun control in wake of Va. shootings; Pentagon conforms ISIS threat to match WH narrative
August 27, 2015 08:37 AM by Doug Powers
The video of Carly Fiorina TKOing Hillary & Tingles should be required viewing for the GOP field
August 7, 2015 02:02 PM by Doug Powers
Sound familiar? Democrats blame people who made a video for horrific acts of others
July 22, 2015 10:06 PM by Doug Powers
'Laugher' curve: Paul Krugman advises US how to avoid Greece-style demise (conservative economics = bad)
July 9, 2015 09:41 PM by Doug Powers
Categories: Paul Krugman, Politics


text:
With No Rings Till The End Of The Year Star Wars saga has new secrets Drew Goddart opened 3 mysteries about Martian MORE ›
Lyrics/song texts are property and copyright of their owners and provided for educational purposes only.
Triangle Lyrics by Nadia Ali
Triangle by Nadia Ali
But how could she ever let Jack go
It's obvious everyone can see
The trouble with this trilogy
Hearts don't come...
In sets of three So what do they do now?
There's only one way to find out
It's time to pick your prize and
It better be right, it better be right
This triangle has
To untangle
Got to let it go
This triangle is
Too much to handle
Got to let it go
Jane loves Joe, but Joe's with Jill
But Jane wants to be with Joe still
It's bad enough it breaks Jack's heart
It's tearing their whole world apart
But how do you stop
When it's gone so far


text:
Positions in the health sector are expected to have the brightest job prospects in the region.
- Filed Under
Taking care of the Southern Tier region's health - physical and financial - and our infrastructure will drive job creation through the rest of the decade.
Three years into the decade of the '10s, a look at the New York State Department of Labor's report of labor prospects for 2010-2020 show those trends, helped to be set by the baby boom generation.
"We have baby boomers influencing every facet of the economy at this point. Every day, 10,000 more boomers turn 65," said Christian Harris, labor market analyst for the Southern Tier Region of the New York State Department of Labor's Division of ...


text:
Poet and author Alejandro Murguía gives his inaugural poet laureate address titled: The Parallel Literary Histories of San Francisco - Poetry in Times of Hope and Resistance. A poet, editor, translator, literary organizer and educator, Murguía is the 6th Poet Laureate of San Francisco.
1 p.m. – Koret Auditorium, San Francisco Main Library
Opening Ceremony: Jorge Molina, Shaman of the Mission
Native American Invocation: Dr. José Cuellar, Professor Emeritus, San Francisco State University
Welcome: San Francisco City Librarian Luis Herrera
Introduction: Byron Spooner, Friends of the San Francisco Public Library and Poet Roberto Vargas
Inaugural Address: Alejandro Murguía
2 p.m. Reception – Latino/Hispanic Community Meeting Room, San Francisco Main Library
Entertainment by La Familia Pena Govea
A book sale by Readers bookstore follows his address.
Upcoming Events
- Delicious Desserts: Alice Medrich speaks
- Tuesday, October 13, 2015, 3:00 pmMain Library, Koret Auditorium
- Slavery: Ancient Greece and Rome vs. the American South
- Wednesday, October 14, 2015, 7:00 pmMerced, Merced General Floor Area
- Between His Walking Words/Entre Sus Palabras Andantes
- Sunday, October 18, 2015, 3:00 pmMain Library, Latino/Hispanic Rms A & B


text:
Pump up your pumpkin with these cute'n'creative designs
6 little signs your crush is crushing right back
The coolest pics of last week's supermoon
Exclusive: GL's got your first look at the Girl Meets World and K.C. Undercover Halloween episodes
Stop monkeying around and try this banana nut spread
6 fab food bags to rock with your costume (and beyond)
Nail polish expires? The *real* shelf-life of your fave beauty products
#Mmmonday: The all-time best after-school snacks
Sneak a peek at our awesome October/November issue starring Bea Miller!
GL's Exclusive Look at GMW's "Girl Meets World of Terror 2"
More Friends = More Fun
GL Tweets !
10 HOURS AGO Yes, you CAN stop biting your nails. Here's how: http://t.co/77zPcujlY0 pic.twitter.com/xM9DHQs9RW
11 HOURS AGO What's better than boots? (Hint: Nothing): http://t.co/BFSqjY9GKn pic.twitter.com/R9tycy2JF8
12 HOURS AGO 5 reasons you should join theatre right now: http://t.co/iHztxihA09 pic.twitter.com/ImkHiSUZ9s
sponsored links
Check these out, too...
Pull yourself together
One of the first things you should do in your back-to-school
prep is get organized! Whether you recycle your binders from last year (very
earth-friendly!) or get new ones, label each of them clearly. Make sure you
have extra paper and a specific binder or folder for each class, so your
schoolwork doesn't get jumbled together. If you can't find that math worksheet,
how will you ever expect to complete it? You can even assign a different
colored highlighter to use for each class, or decorate the binders to make them
more fun! The more organized you are, the easier it'll be to get that work
Create a schedule
We know you're busy, but if you make a study schedule,
you'll be way more likely to actually sit down and do your work. Keeping a
schedule will let you plan out the day and stay on track, which means you'll
still have time to do all your favorite things. Time management is one of the
keys to success, so if you start now, you'll be in great shape for the future.
Form a study group
Be sure to pencil some group study time into your schedule.
Studying with friends can be both helpful and productive, so call your buddies
before that big science test that you've been stressing over. You can alternate
whose house you use, which will give you a new environment each time and make
the studying less boring. Another
advantage of including your friends? You'll have instant help if you get stuck
on a homework problem, which means fewer struggles and more success!
Ask your friends
POSTED IN studying secrets, grades, boost your grades, smart girl secrets, get all A's this year
GIVEAWAY: Fab up your life with these *free* fall finds!
Want to score the best books, beauty and other bounty this season? Of course you do!
CLICK HERE for your chance to win.


text:
The six-year DRIVE Act would be the first multi-year bill since 2012's MAP-21, which was just a two-year funding measure. The bill also is packed full of regulatory changes, with some notable stabs by Congress at the CSA carrier-scoring program.Read More
Changes to driver drug testing rules, allowance of under-21 interstate drivers and removal of CSA scores from public view are all included, among other provisions.Read More
In addition, the Federal Motor Carrier Safety Administration is proposing several enhancements for its Safety Measurement System, which the agency uses to measure the safety of motor carriers.Read More
Should carriers' CSA SMS percentile rankings/scores be removed from public view? Weigh in via this poll.Read More
The Transportation Intermediaries Association has become the latest organization to call on the DOT to remove from public view the carrier percentile rankings in the Compliance, Safety, Accountability trucking regulatory program, saying it has "serious concerns" about the scores' methodology and correlation (or lack thereof) to crash risk.Read More
New House bill 1371 would pull carrier CSA scores from public view, require FMCSA to revamp program.Read More
Susan Fleming of the Government Accountability Office said FMCSA's smartphone app release this week, which highlights carriers' CSA ratings, again exposed the need to remove the scores from public view.Read More
The bill, TIA says, could limit the role of FMCSA's Compliance, Safety, Accountability program and its use by third parties to hire or otherwise make judgments about trucking companies.Read More
The bill aims to remove the public assumption that carrier rankings in the DOT's Compliance, Safety, Accountability program should be used as a tool to hire carriers.Read More
If you think the FMCSA's Compliance, Safety, Accountability program has misdirected carriers' safety focus in a big way, you'll find a friend in Oregon DOT's David McKane.Read More